李群方法用于黎曼批量归一化
A Lie Group Approach to Riemannian Batch Normalization
AI总结：
本文提出一个基于李群的统一黎曼批量归一化框架，适用于对称正定流形，通过参数化李群族诱导归一化层，在雷达识别、动作识别和EEG分类中验证了有效性。
摘要：
流形值测量存在于计算机视觉和机器学习的众多应用中。近期研究已将深度神经网络（DNN）扩展到流形，同时归一化技术也被适配到多种流形，称为黎曼归一化。然而，现有的大多数黎曼归一化方法是以临时方式推导的，仅适用于特定流形。本文在李群上建立了黎曼批量归一化（RBN）技术的统一框架。我们的框架提供了控制黎曼均值和方差的理论保证。在实验上，我们聚焦于对称正定（SPD）流形，其具有三种不同类型的李群结构。利用形变概念，我们将SPD流形上的现有李群推广为三族参数化李群。随后，针对SPD神经网络提出了由这些李群诱导的特定归一化层。我们通过三组实验证明了我们方法的有效性：雷达识别、人体动作识别和脑电图（EEG）分类。代码可在 https://github.com/GitZH-Chen/LieBN.git 获取。
英文摘要：
Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been adapted to several manifolds, referred to as Riemannian normalization. Nonetheless, most of the existing Riemannian normalization methods have been derived in an ad hoc manner and only apply to specific manifolds. This paper establishes a unified framework for Riemannian Batch Normalization (RBN) techniques on Lie groups. Our framework offers the theoretical guarantee of controlling both the Riemannian mean and variance. Empirically, we focus on Symmetric Positive Definite (SPD) manifolds, which possess three distinct types of Lie group structures. Using the deformation concept, we generalize the existing Lie groups on SPD manifolds into three families of parameterized Lie groups. Specific normalization layers induced by these Lie groups are then proposed for SPD neural networks. We demonstrate the effectiveness of our approach through three sets of experiments: radar recognition, human action recognition, and electroencephalography (EEG) classification. The code is available at https://github.com/GitZH-Chen/LieBN.git.
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